Identifier
Values
[1,0] => [2,1] => [2,1] => [1,2] => 0
[1,0,1,0] => [3,1,2] => [3,2,1] => [2,1,3] => 0
[1,1,0,0] => [2,3,1] => [3,2,1] => [2,1,3] => 0
[1,0,1,0,1,0] => [4,1,2,3] => [4,2,3,1] => [2,3,1,4] => 0
[1,0,1,1,0,0] => [3,1,4,2] => [4,2,3,1] => [2,3,1,4] => 0
[1,1,0,0,1,0] => [2,4,1,3] => [3,4,1,2] => [4,1,2,3] => 0
[1,1,0,1,0,0] => [4,3,1,2] => [4,3,2,1] => [3,2,1,4] => 0
[1,1,1,0,0,0] => [2,3,4,1] => [4,2,3,1] => [2,3,1,4] => 0
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [5,2,3,4,1] => [2,3,4,1,5] => 1
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [5,2,3,4,1] => [2,3,4,1,5] => 1
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [4,2,5,1,3] => [2,5,1,3,4] => 1
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [5,2,4,3,1] => [2,4,3,1,5] => 0
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [5,2,3,4,1] => [2,3,4,1,5] => 1
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [3,5,1,4,2] => [5,1,4,2,3] => 0
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [3,5,1,4,2] => [5,1,4,2,3] => 0
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [5,4,3,2,1] => [4,3,2,1,5] => 0
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [5,4,3,2,1] => [4,3,2,1,5] => 0
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [5,3,2,4,1] => [3,2,4,1,5] => 0
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [4,2,5,1,3] => [2,5,1,3,4] => 1
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [4,5,3,1,2] => [5,3,1,2,4] => 0
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [5,4,3,2,1] => [4,3,2,1,5] => 0
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,2,3,4,1] => [2,3,4,1,5] => 1
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [6,2,3,4,5,1] => [2,3,4,5,1,6] => 2
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [6,2,3,4,5,1] => [2,3,4,5,1,6] => 2
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [5,2,3,6,1,4] => [2,3,6,1,4,5] => 2
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [6,2,3,5,4,1] => [2,3,5,4,1,6] => 1
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [6,2,3,4,5,1] => [2,3,4,5,1,6] => 2
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [4,2,6,1,5,3] => [2,6,1,5,3,4] => 1
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [4,2,6,1,5,3] => [2,6,1,5,3,4] => 1
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [6,2,5,4,3,1] => [2,5,4,3,1,6] => 0
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [6,2,5,4,3,1] => [2,5,4,3,1,6] => 0
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [6,2,4,3,5,1] => [2,4,3,5,1,6] => 1
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [5,2,3,6,1,4] => [2,3,6,1,4,5] => 2
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [5,2,6,4,1,3] => [2,6,4,1,3,5] => 1
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [6,2,5,4,3,1] => [2,5,4,3,1,6] => 0
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [6,2,3,4,5,1] => [2,3,4,5,1,6] => 2
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [3,6,1,4,5,2] => [6,1,4,5,2,3] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [3,6,1,4,5,2] => [6,1,4,5,2,3] => 0
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [3,5,1,6,2,4] => [5,1,6,2,4,3] => 0
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [3,6,1,4,5,2] => [6,1,4,5,2,3] => 0
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [6,4,3,2,5,1] => [4,3,2,5,1,6] => 0
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [6,4,3,2,5,1] => [4,3,2,5,1,6] => 0
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [6,5,3,4,2,1] => [5,3,4,2,1,6] => 0
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [6,5,3,4,2,1] => [5,3,4,2,1,6] => 0
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [6,4,3,2,5,1] => [4,3,2,5,1,6] => 0
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [5,3,2,6,1,4] => [3,2,6,1,4,5] => 1
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [6,5,3,4,2,1] => [5,3,4,2,1,6] => 0
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [6,5,3,4,2,1] => [5,3,4,2,1,6] => 0
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [6,3,2,4,5,1] => [3,2,4,5,1,6] => 1
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [4,2,6,1,5,3] => [2,6,1,5,3,4] => 1
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [4,2,6,1,5,3] => [2,6,1,5,3,4] => 1
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [4,6,5,1,3,2] => [6,5,1,3,2,4] => 0
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [4,6,5,1,3,2] => [6,5,1,3,2,4] => 0
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [4,6,3,1,5,2] => [6,3,1,5,2,4] => 0
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [6,5,4,3,2,1] => [5,4,3,2,1,6] => 0
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [6,5,4,3,2,1] => [5,4,3,2,1,6] => 0
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [6,5,4,3,2,1] => [5,4,3,2,1,6] => 0
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [6,4,3,2,5,1] => [4,3,2,5,1,6] => 0
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [5,2,3,6,1,4] => [2,3,6,1,4,5] => 2
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [5,2,6,4,1,3] => [2,6,4,1,3,5] => 1
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [5,6,4,3,1,2] => [6,4,3,1,2,5] => 0
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [6,5,4,3,2,1] => [5,4,3,2,1,6] => 0
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [2,3,4,5,1,6] => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [7,2,3,4,5,6,1] => [2,3,4,5,6,1,7] => 3
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [7,2,3,4,5,6,1] => [2,3,4,5,6,1,7] => 3
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [6,2,3,4,7,1,5] => [2,3,4,7,1,5,6] => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [7,2,3,4,5,6,1] => [2,3,4,5,6,1,7] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [6,2,3,4,7,1,5] => [2,3,4,7,1,5,6] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [7,2,3,4,5,6,1] => [2,3,4,5,6,1,7] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [7,2,6,5,4,3,1] => [2,6,5,4,3,1,7] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [7,2,6,5,4,3,1] => [2,6,5,4,3,1,7] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [7,2,6,5,4,3,1] => [2,6,5,4,3,1,7] => 0
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [6,2,3,4,7,1,5] => [2,3,4,7,1,5,6] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => [7,2,6,5,4,3,1] => [2,6,5,4,3,1,7] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [7,2,3,4,5,6,1] => [2,3,4,5,6,1,7] => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [7,6,3,4,5,2,1] => [6,3,4,5,2,1,7] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [7,6,3,4,5,2,1] => [6,3,4,5,2,1,7] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [7,6,3,4,5,2,1] => [6,3,4,5,2,1,7] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [7,6,3,5,4,2,1] => [6,3,5,4,2,1,7] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => [7,6,3,5,4,2,1] => [6,3,5,4,2,1,7] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [7,6,3,5,4,2,1] => [6,3,5,4,2,1,7] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => [7,6,3,5,4,2,1] => [6,3,5,4,2,1,7] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [7,6,3,5,4,2,1] => [6,3,5,4,2,1,7] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => [7,5,4,3,2,6,1] => [5,4,3,2,6,1,7] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => [7,5,4,3,2,6,1] => [5,4,3,2,6,1,7] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [7,5,4,3,2,6,1] => [5,4,3,2,6,1,7] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1,7] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1,7] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1,7] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [7,5,4,3,2,6,1] => [5,4,3,2,6,1,7] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => [7,6,4,3,5,2,1] => [6,4,3,5,2,1,7] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1,7] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1,7] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => [7,5,4,3,2,6,1] => [5,4,3,2,6,1,7] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [6,2,3,4,7,1,5] => [2,3,4,7,1,5,6] => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1,7] => 0
>>> Load all 226 entries. <<<
[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [2,3,4,5,6,1,7] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,7,1,8] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,7,1,8] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,7,1,8] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,7,1,8] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,7,1,8] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,7,1,8] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [3,5,1,7,2,8,4,6] => [5,1,7,2,8,4,6,3] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,8,3,7,5,6] => [3,5,1,8,2,7,6,4] => [5,1,8,2,7,6,4,3] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,6,1,5,3,8,4,7] => [3,7,1,5,4,8,2,6] => [7,1,5,4,8,2,6,3] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1,8,6,3,5,7] => [3,6,1,8,7,2,5,4] => [6,1,8,7,2,5,4,3] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,8,7,3,5,6] => [3,6,1,8,7,2,5,4] => [6,1,8,7,2,5,4,3] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,8,1,5,6,3,4,7] => [3,8,1,7,6,5,4,2] => [8,1,7,6,5,4,2,3] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,8,1,5,7,3,4,6] => [3,8,1,7,6,5,4,2] => [8,1,7,6,5,4,2,3] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,8,1,7,6,3,4,5] => [3,8,1,7,6,5,4,2] => [8,1,7,6,5,4,2,3] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1,8,6,7,3,5] => [3,7,1,8,6,5,2,4] => [7,1,8,6,5,2,4,3] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,8,1,5,6,7,3,4] => [3,8,1,7,6,5,4,2] => [8,1,7,6,5,4,2,3] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,3,1,6,2,8,5,7] => [5,3,2,7,1,8,4,6] => [3,2,7,1,8,4,6,5] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3,1,8,2,7,5,6] => [5,3,2,8,1,7,6,4] => [3,2,8,1,7,6,4,5] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8,7,1,5,2,3,4,6] => [8,7,3,6,5,4,2,1] => [7,3,6,5,4,2,1,8] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8,7,1,6,2,3,4,5] => [8,7,3,6,5,4,2,1] => [7,3,6,5,4,2,1,8] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8,4,1,6,2,7,3,5] => [8,7,3,6,5,4,2,1] => [7,3,6,5,4,2,1,8] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [6,8,1,5,2,7,3,4] => [8,7,3,6,5,4,2,1] => [7,3,6,5,4,2,1,8] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [4,3,1,8,6,2,5,7] => [6,3,2,8,7,1,5,4] => [3,2,8,7,1,5,4,6] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [4,3,1,8,7,2,5,6] => [6,3,2,8,7,1,5,4] => [3,2,8,7,1,5,4,6] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,1,5,6,2,3,7] => [8,7,3,6,5,4,2,1] => [7,3,6,5,4,2,1,8] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8,4,1,5,7,2,3,6] => [8,7,3,6,5,4,2,1] => [7,3,6,5,4,2,1,8] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8,4,1,7,6,2,3,5] => [8,7,3,6,5,4,2,1] => [7,3,6,5,4,2,1,8] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => [8,7,3,6,5,4,2,1] => [7,3,6,5,4,2,1,8] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,3,1,8,6,7,2,5] => [7,3,2,8,6,5,1,4] => [3,2,8,6,5,1,4,7] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8,3,1,5,6,7,2,4] => [8,7,3,6,5,4,2,1] => [7,3,6,5,4,2,1,8] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8,4,1,5,6,7,2,3] => [8,7,3,6,5,4,2,1] => [7,3,6,5,4,2,1,8] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,6,4,1,3,8,5,7] => [4,7,5,1,3,8,2,6] => [7,5,1,3,8,2,6,4] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,8,4,1,3,7,5,6] => [4,8,5,1,3,7,6,2] => [8,5,1,3,7,6,2,4] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,6,5,1,3,8,4,7] => [4,7,5,1,3,8,2,6] => [7,5,1,3,8,2,6,4] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,8,4,1,6,3,5,7] => [4,8,6,1,7,3,5,2] => [8,6,1,7,3,5,2,4] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,8,4,1,7,3,5,6] => [4,8,6,1,7,3,5,2] => [8,6,1,7,3,5,2,4] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,8,5,1,6,3,4,7] => [4,8,7,1,6,5,3,2] => [8,7,1,6,5,3,2,4] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,8,5,1,7,3,4,6] => [4,8,7,1,6,5,3,2] => [8,7,1,6,5,3,2,4] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,7,8,1,6,3,4,5] => [4,8,7,1,6,5,3,2] => [8,7,1,6,5,3,2,4] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,8,4,1,6,7,3,5] => [4,8,7,1,6,5,3,2] => [8,7,1,6,5,3,2,4] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,8,5,1,6,7,3,4] => [4,8,7,1,6,5,3,2] => [8,7,1,6,5,3,2,4] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,3,4,1,2,8,5,7] => [7,5,4,3,2,8,1,6] => [5,4,3,2,8,1,6,7] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [8,3,4,1,2,7,5,6] => [8,5,4,3,2,7,6,1] => [5,4,3,2,7,6,1,8] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,5,1,2,8,4,7] => [7,5,4,3,2,8,1,6] => [5,4,3,2,8,1,6,7] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,4,1,2,3,5,6] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1,8] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8,7,5,1,2,3,4,6] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1,8] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,7,8,1,2,3,4,5] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1,8] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,5,4,1,2,8,3,7] => [7,5,4,3,2,8,1,6] => [5,4,3,2,8,1,6,7] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,4,1,2,7,3,6] => [8,7,5,4,3,6,2,1] => [7,5,4,3,6,2,1,8] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,8,4,1,2,7,3,5] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1,8] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [6,8,5,1,2,7,3,4] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1,8] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,3,4,1,6,2,5,7] => [8,6,4,3,7,2,5,1] => [6,4,3,7,2,5,1,8] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8,3,4,1,7,2,5,6] => [8,6,4,3,7,2,5,1] => [6,4,3,7,2,5,1,8] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,5,4,1,6,2,3,7] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1,8] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8,5,4,1,7,2,3,6] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1,8] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,8,4,1,6,2,3,5] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1,8] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,8,5,1,6,2,3,4] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1,8] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5] => [8,7,4,3,6,5,2,1] => [7,4,3,6,5,2,1,8] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8,3,5,1,6,7,2,4] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1,8] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8,5,4,1,6,7,2,3] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1,8] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,8,4,6,1,3,5,7] => [5,8,6,7,1,3,4,2] => [8,6,7,1,3,4,2,5] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,7,4,8,1,3,5,6] => [5,8,6,7,1,3,4,2] => [8,6,7,1,3,4,2,5] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,8,6,5,1,3,4,7] => [5,8,7,6,1,4,3,2] => [8,7,6,1,4,3,2,5] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,8,5,1,3,4,6] => [5,8,7,6,1,4,3,2] => [8,7,6,1,4,3,2,5] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7,8,6,1,3,4,5] => [5,8,7,6,1,4,3,2] => [8,7,6,1,4,3,2,5] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,6,4,5,1,8,3,7] => [5,7,4,3,1,8,2,6] => [7,4,3,1,8,2,6,5] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,6,1,7,3,5] => [5,8,7,6,1,4,3,2] => [8,7,6,1,4,3,2,5] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,6,5,1,7,3,4] => [5,8,7,6,1,4,3,2] => [8,7,6,1,4,3,2,5] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,3,4,6,1,2,5,7] => [8,6,5,7,3,2,4,1] => [6,5,7,3,2,4,1,8] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,3,4,8,1,2,5,6] => [8,6,5,7,3,2,4,1] => [6,5,7,3,2,4,1,8] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,3,6,5,1,2,4,7] => [8,6,7,5,4,2,3,1] => [6,7,5,4,2,3,1,8] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,3,8,5,1,2,4,6] => [8,6,7,5,4,2,3,1] => [6,7,5,4,2,3,1,8] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,8,6,1,2,4,5] => [8,6,7,5,4,2,3,1] => [6,7,5,4,2,3,1,8] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,6,4,5,1,2,3,7] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,8,4,5,1,2,3,6] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,8,4,6,1,2,3,5] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,6,5,1,2,3,4] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,4,5,1,8,2,7] => [7,5,4,3,2,8,1,6] => [5,4,3,2,8,1,6,7] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8,3,4,5,1,7,2,6] => [8,7,5,4,3,6,2,1] => [7,5,4,3,6,2,1,8] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8,3,4,6,1,7,2,5] => [8,7,5,6,3,4,2,1] => [7,5,6,3,4,2,1,8] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8,3,6,5,1,7,2,4] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8,6,4,5,1,7,2,3] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,4,7,6,1,3,5] => [6,8,7,5,4,1,3,2] => [8,7,5,4,1,3,2,6] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [6,8,7,5,4,1,3,2] => [8,7,5,4,1,3,2,6] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1,8] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8,3,4,5,7,1,2,6] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1,8] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8,3,4,7,6,1,2,5] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8,3,7,5,6,1,2,4] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,7,4,5,6,1,2,3] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1,8] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8,3,4,5,6,7,1,2] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1,8] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,7,1,8] => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,1,2,3,4,5,6,7,8] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1,9] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,1,2,3,4,5,6,9,7] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1,9] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,1,2,3,4,5,8,9,6] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1,9] => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1,9] => 5
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,6,7,8,9,4] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1,9] => 5
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,3] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1,9] => 5
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1,9] => 5
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [9,8,5,1,7,2,3,4,6] => [9,8,7,4,6,5,3,2,1] => [8,7,4,6,5,3,2,1,9] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,1,6,2,3,4,5] => [9,8,7,4,6,5,3,2,1] => [8,7,4,6,5,3,2,1,9] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [9,5,4,1,8,7,2,3,6] => [9,8,7,4,6,5,3,2,1] => [8,7,4,6,5,3,2,1,9] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [9,8,4,5,1,2,3,6,7] => [9,8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,9] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [9,8,6,5,1,2,3,4,7] => [9,8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,9] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,6,1,2,3,4,5] => [9,8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,9] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [9,7,4,5,6,1,2,3,8] => [9,8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,9] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [8,9,4,5,6,1,2,3,7] => [9,8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,9] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,9,7,5,6,1,2,3,4] => [9,8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,9] => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [9,3,7,5,6,1,8,2,4] => [9,8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,9] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9,8,4,5,6,7,1,2,3] => [9,8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,9] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1,9] => 5
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1,10] => 6
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,10,3] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1,10] => 6
[] => [1] => [1] => [1] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [10,9,8,7,5,6,4,3,2,1] => [9,8,7,5,6,4,3,2,1,10] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [8,9,4,5,10,1,2,3,6,7] => [10,9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1,10] => 0
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [10,3,8,5,6,7,1,9,2,4] => [10,9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1,10] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [10,9,4,5,6,7,8,1,2,3] => [10,9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1,10] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1,10] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1,10] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1,10] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,1,2,3,4,5,6,9,10,7] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1,10] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,1,2,3,4,5,8,9,10,6] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1,10] => 6
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,1,2,3,4,7,8,9,10,5] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1,10] => 6
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,1,2,3,6,7,8,9,10,4] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1,10] => 6
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Description
The number of occurrences of the vincular pattern |12-3 in a permutation.
This is the number of occurrences of the pattern $123$, where the first matched entry is the first entry of the permutation and the other two matched entries are consecutive.
In other words, this is the number of ascents whose bottom value is strictly larger than the first entry of the permutation.
Map
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
Map
Inverse Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.